State Evaluation of Electrical Equipment in Substations Based on Data Mining

Abstract

This paper explores the combination of a data mining-based state evaluation method for electrical equipment in substations, analyzing the effectiveness and accuracy. First, a Gaussian mixture model is applied to fit all raw data of electrical equipment. The Expectation Maximization algorithm summarizes the data distribution characteristics and identifies outliers. The a priori algorithm is then employed for data mining to derive frequent itemsets and association rules between equipment quality and measurement data. For new equipment samples, conditional probabilities of each feature are independently calculated and combined to classify and evaluate equipment quality. The results suggest that equipment reliability in smart substations can be inferred from historical and real-time operational data using improved association rule algorithms and Naive Bayes classifiers. Finally, the proposed method was applied to analyze statistical data from a 110 kV substation of a power supply company. The states prediction accuracy exceeded 95% when compared with actual equipment quality. The effectiveness evaluation metrics demonstrated that this method outperforms single-category algorithms in terms of accuracy and discrimination ability.

1. Introduction

Smart substations, essential to modern power transmission and distribution systems, face complex challenges in equipment status assessment. Rapid artificial intelligence (AI) advancements have improved substation equipment monitoring and evaluation, enhancing system reliability and efficiency. AI technology robustly supports the safe and economic operation of modern power systems.

Smart substations generate vast amounts multidimensional operational data, including temperature, mechanical parameters, and power load. Traditional manual analysis methods are time-consuming and error prone. AI algorithms efficiently process data through data mining and machine learning, transforming raw data into valuable insights. Ref. [1] proposes that recurrent neural networks (RNNs) can capture dynamic equipment status changes in substation operational time-series data. This improves data processing speed and state assessment accuracy, aiding fault diagnosis. Ref. [2] employs a self-organizing map (SOM) to analyze the comprehensive value of transformer fault gas. AI can pre-emptively identify fault risks and issue early warnings. AI and data fusion techniques enable multisource data analysis [3]. For instance, combining temperature anomaly detection and vibration data analysis enables more accurate differentiation between internal faults and environmental factors. AI models autonomously update parameters based on operational data, adapting to new environments and fault modes. This enables intelligent substations to effectively manage operational uncertainties [4]. Artificial intelligence algorithms significantly reduce unplanned downtime through real-time monitoring and precise evaluation, outperforming traditional manual inspection and maintenance [5].

State evaluation is crucial for smart substation operations, ensuring grid safety, reliability, and efficiency. Continuous optimization of data mining, big data analysis and AI technology can further enhance intelligent substations performance and robustness. Ref. [6] proposed a fault assessment method for measurement and control devices based on the Markov model, using spectral clustering to evaluate substation equipment reliability. The model incorporates hardware, software, auxiliary equipment, and human-related faults. Spectral clustering analysis learns key point similarities, generates charts, and performs data clustering. A multidimensional fuzzy comprehensive evaluation method was proposed for online substation equipment monitoring, based on comparisons of data quality methods [7,8]. The method establishes a two-layer data evaluation set, fuzzy relationship matrices and data weights to quantitatively score online monitoring data, demonstrating effectiveness. Ref. [9] points out that substation operation and maintenance inspections generate substantial data while ensuring normal equipment operation. The study elaborates on data mining applications in daily inspections, defect management, and fault analysis. Future equipment status and monitoring data are predicted using trend extrapolation, predictive modeling, and least squares regression. A Lyapunov prediction model for equipment defects and malfunctions is developed using historical data and case studies. Inspection datasets serve as test sets for defect or malfunction prediction, enabling continuous model refinement. Analyzing equipment status using image data and deep convolutional neural networks (CNNs) is viable for intelligent substation equipment evaluation [10]. Multisource monitoring using edge computing and CNNs enhances efficiency in comprehensive substation equipment health evaluation. YOLOv4 incorporates CSPNet, enhancing relevant feature channels while suppressing less important ones. Additionally, PANet utilizes depth-wise separable convolution, enhancing efficiency and evaluation performance. Ref. [11] proposed an electrical equipment defect detection method based on clustering analysis and a priori algorithm. The study employs graph computing to construct an automatic defect identification model for major substation equipment, including transformers and circuit breakers. This model integrates multisource heterogeneous data to assess defect susceptibility across equipment from various manufacturers and production batches. A condition cleaning algorithm eliminates duplicate and false combinations, improving defect detection accuracy and efficiency.

Association rule mining uncovers potential key relationships between database attributes. The a priori algorithm, a prominent association rule method, is widely applied due to its simplicity and efficiency in processing large datasets [12]. However, the basic a priori algorithm often struggles to mine rules of user interest effectively [13,14]. The a priori algorithm typically relies on discretization or frequency thresholding methods when calculating frequent itemsets—it may overlook low-frequency rules with significant correlations [15]. The frequent itemset definition in the a priori algorithm’s rule mining process may result in key rules omission. Recent research proposes methods to improve the a priori algorithm’s handling of continuous data. Combining K-means clustering with the a priori algorithm enhances its applicability and accuracy for continuous data through discretization [16]. Researchers propose using probability distributions for continuous data processing, improving association rule reliability and statistical significance [17]. This approach emphasizes probabilistic modeling in data mining for more accurate and practical rules.

The improved a priori algorithm shows considerable promise in improving the accuracy of electrical equipment state assessments. Further research is warranted to analyze the integration of the enhanced a priori algorithm with the Naive Bayes classifier. The Naive Bayes classifier, renowned for its computational efficiency and simplicity in classification tasks, presents potential enhancements for state evaluation models [18]. The integration of these two methods can enhance the identification of equipment status characteristics while maintaining the detection of crucial rules. The amalgamation of the a priori algorithm and Naive Bayes classifier presents a novel approach to tackling the aforementioned challenges. The Naive Bayes classifier, known for its simplicity and efficiency, effectively mitigates the limitations of the traditional a priori algorithm in classification tasks when integrated [19]. This integrated model facilitates both association rule mining and comprehensive rule classification and analysis, substantially improving the accuracy and reliability of state evaluation.

Table 1. Summary of reference work.

References	Data	Methods	Results	Shortcomings
[2]	Transformer fault gas	SOM	Obtain fault operating conditions and identify components that may cause fault behavior	Single-signal error may affect the final result
[4]	Transformer detection data	Genetic algorithm and association rule	Accurately obtain fault information	No classification when the equipment is not faulty
[5]	Online monitoring information	Fuzzy comprehensive evaluation	Obtain the evaluation level of online monitoring data for substation equipment	Only used online monitoring data
[6]	Devices’ own status and failure rate	Markov model	Learn the similarity of key points, spectral characteristics to complete cluster analysis	Only classified the fault status, lacking advance prediction
[7,8]	Online monitoring data	Multidimensional fuzzy comprehensive evaluation	Grade evaluation of online monitoring data based on quantitative scores	Mainly evaluate data quality without considering specific equipment
[9]	Substation daily inspection data	Lyapunov prediction model	Learning from historical data and similar cases to predict defects or failures	The dataset only includes inspection data, not all data
[10]	Image data	Multisource monitoring and deep CNN	Improved YOLOv4 network for device detection, combined with monitoring data to evaluate status	Utilizes image data, but may not be able to detect defects within the equipment
[11]	Data recording of equipment defects	Cluster analysis and a priori algorithm	Obtain weak links in the same batch of equipment or family defects from equipment manufacturers	Using the device manufacturer dataset without considering the actual environment
[16]	Environmental data and online monitoring data	K-means and alternative clustering methods	Well used in load forecasting, fault detection, power quality analysis, and system security assessment	K-means is sensitive to initialization and may be locally optimal
[17]	Medical data stream	Association rule mining algorithm	Using probability distribution for continuous data, ensuring the reliability of association rules	No data classification description, only searched association rules
[19]	Bank marketing dataset	Association rules and Naive Bayes classifier	Using a priori algorithm to combine relevant attributes to adapt independent assumptions in Naive Bayes classifier	Failed to use in determining the status of electrical equipment

summarizes the latest trends in electrical equipment state evaluation and data mining research.

This paper proposes a data mining-based method for assessing the state of electrical equipment in smart substations. It aims to evaluate the reliability of diverse electrical equipment by analyzing historical and real-time operational data, using a combination of improved association rule algorithms and Naive Bayes classifiers. The method consists of three primary phases: data preprocessing, association rule mining, and equipment classification. A Gaussian mixture model is employed to fit the original dataset, with the expectation-maximization algorithm to summarize data distribution characteristics and filtering outliers. The a priori algorithm is applied to the preprocessed dataset to identify frequent itemsets and derive association rules, which are then used for model training. For new equipment samples, conditional probabilities of each feature are independently calculated and combined. This process enables the evaluation of electrical equipment status. The scheme achieves high computational efficiency by determining crucial operating characteristics of electrical equipment (such as insulation resistance, contact resistance, mechanical properties) and identifying their influence on equipment failure.

The proposed methodology presents several advantages compared to existing electrical equipment status assessment techniques:

• The proposed state assessment algorithm integrates the a priori algorithm with a Naive Bayes classifier. The former efficiently identifies frequent itemset, revealing operational patterns and correlations, including co-occurrence of equipment failures under specific conditions. This provides valuable input for subsequent state classification. The Naive Bayes classifier utilizes the association rules discovered by a priori to swiftly classify device states, enhancing predictive capabilities in specific contexts.
• Gaussian mixture models are employed to unify state characteristics of electrical equipment across varying environments, loads, and operating conditions. These models provide a cohesive description of state features, identifying commonalities and differences across states, offering high flexibility and adaptability. This approach minimizes the impact of environmental interference and varying working conditions on status monitoring data, enhancing the reliability of final evaluation results.

This paper is structured as follows: Section 1 provides a basic introduction, discussing substation development and current trends in electrical equipment evaluation methods. Section 2 presents a comprehensive explanation of the proposed algorithm. It begins by introducing characteristics of substation electrical equipment status assessment, including equipment types and status data acquisition methods. Then, it explores effective information dataset extraction techniques and details the collaborative application of a priori algorithm and Naive Bayes classifiers for device state classification and evaluation. Finally, this section validates the efficacy of the proposed data mining-based smart substation state evaluation method and algorithm. Section 3 summarizes this paper and proposes future research directions.

2. Methodology

This section outlines the stepwise process for developing an electrical equipment state evaluation model, starting with dataset preparation. The initial phase involves preprocessing to consolidate equipment test data, online monitoring data, and human observations. Following preprocessing, clustering and association rule analysis are performed to discern relationships between equipment states (abnormal, intact, or faulty) and anomalous patterns or outliers in the observation data. Based on these analyses, evaluation model rules are formulated to assess the state of electrical equipment in Figure 1.

2.1. Equipment Status Characteristics

A substation’s high-voltage electrical equipment primarily consists of transformers, circuit breakers, voltage transformers, current transformers, surge arresters, and capacitor banks. These devices serve multiple functions: voltage transformation, circuit interruption or connection, high-voltage current/voltage measurement, and lightning overvoltage protection, collectively ensuring stable power transmission and distribution. Substation state evaluation focuses on defining and assessing the current condition of these devices, quantified through testing and online monitoring.

Electrical testing methods evaluate equipment insulation and functionality to determine its operational viability within the system. The predominant method involves comparing current test values with those recorded at equipment delivery or manufacturer-specified ranges. Post-test analysis of deviations from these reference values, coupled with expert assessment, determines equipment condition. Online monitoring utilizes various sensors to capture real-time equipment parameters. The data are transmitted to a monitoring system for assessment by personnel or automated analysis systems. In a substation, the Supervisory Control and Data Acquisition (SCADA) system integrates online monitoring data from various devices via specialized modules. Transformer monitoring data include winding and oil temperature (via temperature sensors), current and voltage (via current transformers and voltage transformers), dissolved gas analysis (via gas chromatography), and insulation status (via insulation monitoring systems). Switchgear monitoring data comprise: switch operation count and status (via position sensors), temperature (via temperature sensors), and operating current (via current transformers). Switchgear cabinet monitoring data encompass internal or external temperature (via temperature sensors), internal humidity (via humidity sensors), and partial discharge (via specialized monitoring devices). Lightning arrester monitoring data include leakage current (via leakage current tester) for performance evaluation and discharge frequency (via discharge counter) to track operational conduction events. Capacitor monitoring primarily focuses on the temperature of capacitors and their peripheral devices, measured via temperature sensors. Cable monitoring data encompass cable sheath and internal temperatures (via temperature sensors), partial discharge (via specialized monitoring devices).

The substation environment influences internal equipment, necessitating regular inspections by operation and maintenance personnel. These inspections focus on aspects beyond automated monitoring, including temperature at contact and wire connection points, inspection of aluminum stranded wire integrity, assessing of plants or animals’ interference environmental temperature and humidity recording, oil level checks in oil-filled equipment, and SF₆ equipment gas pressure monitoring [20,21].

Substations typically employ two transformer types: main power transformer (oil-filled) for voltage exchange and energy distribution, and station power transformers (dry-type) for powering station equipment. Circuit breakers are mainly categorized as gas-insulated switchgear (GIS), SF₆ circuit breakers, oil circuit breakers, and vacuum circuit breakers. GIS or SF₆ circuit breakers are typically employed on the high-voltage side, while switchgear is utilized on the low-voltage side. The three primary transformer types are current transformers, electromagnetic voltage transformers, and capacitive voltage transformers [22,23,24].

Table 2. High-voltage electrical equipment quantification items.

	Tests	Online Monitoring	Human Inspection
Transformer	Winding DC resistance	Temperature and winding temperature	Level, oil color, oil temperature indicator
	Insulation resistance	Partial discharge	Running sound
	Absorption ratio	Oil level
	Winding dielectric loss factor	Chromatography of dissolved gases in oil
	Dielectric loss factor of capacitive bushing	Water content in oil
	Winding and bushing withstand voltage	Gas content in oil
	Voltage ratio of all taps of the winding	Grounding current of iron core or clamp
	No-load current and no-load loss	On-load tap changer monitoring
	Measurement of winding deformation
	No-load closing at full voltage
Circuit breaker	Insulation resistance	Gas pressure	Oil and air leakage
	Voltage withstand test	Opening and closing time	Insulator breakage
	Closing resistance value and closing resistance input time	Spring pressure and stroke	Abnormal operating mechanism
	Synchronicity and time of circuit breaker opening and closing		Temperature of isolation switch contacts and line terminals
	Conductive circuit resistance		Gas pressure
Voltage and current transformers	Insulation resistance	Primary and secondary voltage and current values
	Dielectric loss factor;	Insulation
Cables and bus	Insulation resistance	Partial discharge
	DC withstand voltage test	Joint or busbar temperature
GIS equipment		SF6 gas concentration
		Partial discharge monitoring
Lightning arrester	Insulation resistance	AC leakage current under operating voltage	Operation status of discharge counter
	Leakage current at DC 1ma voltage u1ma and 0.75 u1ma	Operation status of discharge counter
Capacitor bank	Capacitors insulation resistance capacitance	Shell intact
	Inductor insulation resistance DC resistance	Secure wiring
	Discharge coil insulation resistance winding DC resistance	Fuse

delineates the monitoring parameters for each equipment type.

2.2. Data Analysis

The research analyzed three sources of electrical equipment status monitoring data: experiment tests, online monitoring, and human inspections. This section introduces the dataset model.

Due to current technological constraints, numerous electrical equipment tests must be conducted during power outages. The resulting data reflects the inherent properties of the equipment. The status information includes test date, test items, measured values, ambient conditions (temperature and humidity), and potentially analysis results from test personnel [25]. These attributes are categorized into three types: comparison, verification, and destructive testing. For instance, comparing resistance values with factory or previous test values belongs to the comparison category. Polarity and phase checks fall under verification, while various withstand voltage tests are classified as destructive testing.

Online monitoring devices utilize various sensors to collect real-time data during power grid operation. This data represents the operational information of electrical equipment. It encompasses basic parameters (voltage, current, frequency) and advanced metrics (winding and oil temperatures, dissolved gases, circuit breaker operations, contact resistance, operating time, switchgear characteristics, and partial discharge conditions). These attributes are classified into comparison and validation categories. Unlike experimental data, real-time monitoring yields a more extensive dataset. The dataset selectively incorporates data points that significantly deviate from mean values or exhibit anomalous characteristics.

Human inspection data, unlike experimental and online monitoring data, often poses digitization challenges. Quantifiable data is predominantly confined to instrument and meter measurements. Sensory observations (visual, olfactory, tactile) introduce subjectivity in assessments, including evaluations of equipment condition, environmental factors, and potential faunal threats. Despite their inherent subjectivity, these observations often identify issues that may escape detection by experimental or online monitoring methods. A tripartite logical coding system standardizes this subjective data: 1 (affirmative/good), 0 (negative/bad), and 2 (uncertain). This numerical conversion enhances subsequent data processing and analysis.

The data feature mining processes categorize raw data into discrete and continuous values across multiple scales. This feature entry heterogeneity may influence rule establishment. A mixture Gaussian algorithm is employed to discretize values and achieve quantitative similarity [26].

The discretization process of the Gaussian mixture model begins with collecting substation electrical equipment state data. Let the dataset be $X=\{x_1,x_2,\dots ,x_n\}$, where each $x_i$ denotes a sample.

$$X=\left(\begin{array}{ccc}\begin{array}{cc}{x}_{11}& x_{12}\\ x_{21}& x_{22}\end{array}& \cdots & \begin{array}{cc}{x}_{1(m-1)}& x_{1m}\\ x_{2(m-1)}& x_{2m}\end{array}\\ ⋮& \ddots & ⋮\\ \begin{array}{cc}{x}_{(n-1)1}& x_{(n-1)2}\\ x_{n1}& x_{n2}\end{array}& \cdots & \begin{array}{cc}{x}_{(n-1)(m-1)}& x_{(n-1)m}\\ x_{n(m-1)}& x_{nm}\end{array}\end{array}\right)$$

(1)

The ‘fitdist’ function is used to fit the data and select an appropriate probability distribution model.

The Gaussian mixture models (GMM) parameters are initialized via K-Means clustering establishing initial mean ${\mu }_k$, covariance matrix ${\mathsf{\Sigma }}_k$, and mixing coefficient ${\mathsf{\pi }}_k$.

$$\left\{\begin{array}{c}{\mu }_k={\displaystyle \frac{1}{N_k}}\mathsf{\Sigma }{x}_i\\ {\mathsf{\Sigma }}_k={\displaystyle \frac{1}{N_k}}\mathsf{\Sigma }(x_i-{\mu }_k){(x_i-{\mu }_k)}^T\\ {\mathsf{\pi }}_k={\displaystyle \frac{1}{K}}\end{array}\right.$$

(2)

In the E-step of the Expectation Maximization (EM) algorithm, the sample’s probability density function is computed,

$$N\left(x_i|{\mu }_k,{\mathsf{\Sigma }}_k\right)={\displaystyle \frac{\mathrm{e}\mathrm{x}\mathrm{p}[-(x_i-{\mu }_k){\left(x_i-{\mu }_k\right)}^T{\mathsf{\Sigma }}^{-1}/2]}{\sqrt{{\left(2\pi \right)}^k\mathrm{d}\mathrm{e}\mathrm{t}\left(\mathsf{\Sigma }\right)}}}$$

(3)

And the posterior probability of each sample belonging to each Gaussian component is calculated,

$${\gamma }_{ik}={\displaystyle \frac{{\mathsf{\pi }}_{k}N\left(x_i|{\mu }_k,{\mathsf{\Sigma }}_k\right)}{{\sum }_{i=1}^k{\mathsf{\pi }}_{i}N\left(x_i|{\mu }_i,{\mathsf{\Sigma }}_k\right)}}$$

(4)

In the M-step, GMM parameters are updated.

$$\left\{\begin{array}{c}{\mu }_k={\displaystyle \frac{{\sum }_{i=1}^k{\gamma }_{ik}{x}_i}{{\sum }_{i=1}^k{\gamma }_{ik}}}\\ {\mathsf{\Sigma }}_k={\displaystyle \frac{{\sum }_{i=1}^k({\gamma }_{ik}{x}_i-{\mu }_k){\left(x_i-{\mu }_k\right)}^T}{{\sum }_{i=1}^k{\gamma }_{ik}}}\\ {\mathsf{\pi }}_k={\displaystyle \frac{{\sum }_{i=1}^k{\gamma }_{ik}}{n}}\end{array}\right.$$

(5)

Figure 2 illustrates the data preprocessing workflow. This process integrates minor data variations and independent data unrelated to other features. The main goals are to maintain inter-data feature correspondences and achieve approximate sample size parity across features.

2.3. Association Rules

Equipment status analysis and evaluation involve identifying co-occurring features and isolating relevant elements from the broader feature set. Association rules are then derived to clarify relationships between equipment statuses, facilitating current assessment and future prediction based on real-time data.

For this purpose, the a priori algorithm is employed. The a priori algorithm iteratively generates candidate itemsets, comparing them against a predetermined threshold for requirement fulfillment. This process continues until all possible itemsets re-evaluated and frequent itemsets are identified [27,28,29].

The initial step involves extracting frequent itemsets from the dataset. Given k candidate items in the overall itemset, the itemset is defined as $I=\{i_1,i_2,\dots ,i_k\}$. The candidate itemset 1 for the first iteration is $C_1=\{\left\{i_1\right\},\left\{i_2\right\},\dots ,\{i_k\left\}\right\}$.

After creating the candidate set, the algorithm scans the transaction database to compute support values for each candidate itemset.

$$support\left(\left\{i_k\right\}\right)={\displaystyle \frac{scount\left(\right\{i_k\left\}\right)}{\left|D\right|}}$$

(6)

It can be understood as the ratio of the number $count\left(\right\{i_k\left\}\right)$ containing the set of items to the total number $\left|D\right|$. Then, record all items with support value greater than or equal to the threshold $minsup$ as frequent 1 itemset

$$L_1=\left\{\right\{i_k\}\in C_1|support\left(\left\{i_k\right\}\right)\ge minsup\}$$

(7)

Assuming $L_1=\{\left\{j_1\right\},\left\{j_2\right\},\dots ,\{j_m\left\}\right\}$, a candidate 2-itemset $C_2=\{\left\{j_1,j_2\right\},\left\{j_1,j_3\right\},\left\{j_1,j_4\right\},\dots ,\{j_{\mathrm{m}-1},j_{\mathrm{m}}\}$ generated from $L_1$. Similarly, the support for each candidate itemset is calculated

$$support\left(\left\{j_{\mathrm{m}-1},j_{\mathrm{m}}\right\}\right)={\displaystyle \frac{scount\left(\right\{\left\{j_{\mathrm{m}-1},j_{\mathrm{m}}\right\}\left\}\right)}{\left|D\right|}}$$

(8)

All items with support greater than or equal to the threshold $minsup$ are recorded as frequent itemsets

$$L_2=\{\left\{j_{\mathrm{m}-1},j_{\mathrm{m}}\right\}\in C_2|support\left(\left\{j_{\mathrm{m}-1},j_{\mathrm{m}}\right\}\right)\ge minsup\}$$

(9)

This process iterates until $L_{\mathrm{k}}=\mathrm{\varnothing }$ or $C_{\mathrm{k}}=\mathrm{\varnothing }$, completing frequent itemset generation. The final frequent itemset $L=L_1\cup L_2\cup L_3\cup \dots L_i$ is the union of all $L_i$. Figure 3 illustrates this process flow.

Association rules are calculated for itemset $x_1$ given the occurrence of itemset $x_2$. Multiple indicators are used to evaluate these rules.

Confidence, or conditional probability in statistics, indicates the correlation degree between two itemsets [30]. It is mathematically expressed as

$$Confidence\left(x_2\to x_1\right)={\displaystyle \frac{Support\left(\right\{x_1,x_2\left\}\right)}{Support\left(\right\{x_2\left\}\right)}}$$

(10)

The algorithm sets a minimum confidence threshold, $minconf$. When the confidence level is higher than $minconf$ value, the association rules are considered acceptable and further evaluated using other indicators.

Lift, another evaluation metric, is calculated as

$$Lift\left(x_2\to x_1\right)={\displaystyle \frac{Confidence\left(x_2\to x_1\right)}{Support\left(\right\{x_1\left\}\right)}}$$

(11)

A lift value is greater than one indicates a positive correlation, suggesting $x_2$’s occurrence increases $x_1$’s likelihood [13,31]. This metric helps determine the association strength between itemsets.

Cosine similarity, often used to define rule strength, is calculated as:

$$Cosine\left(x_2\to x_1\right)={\displaystyle \frac{Support\left(\right\{x_1,x_2\left\}\right)}{\sqrt{Support\left(\right\{x_1\left\}\right)\times Support\left(\right\{x_2\left\}\right)}}}$$

(12)

Values range from zero to one, with higher values indicating stronger association rules.

2.4. Methods of State Evaluation of Electrical Equipment

Each record is labeled based on the data recording device’s current status (e.g., intact, attentive, abnormal). If the device’s current status is indeterminate, it is marked as ‘uncertain’. The a priori algorithm is applied to discover association rules for state evaluation using labeled historical data. Discovered rules are evaluated using the aforementioned indicators to identify the most significant. Equipment status assessment accuracy is analyzed and estimated using historical evaluation data.

For state judgment, ri denotes the prerequisite length of each association rule, where i is the rule number, reflecting dataset-specific rules. The $cover$ is defined as the ratio of items between two different datasets in the same state. The state–dataset relationship is analyzed based on these criteria:

• Combine association rules with higher $cover$ value for the same state.
• For rules with equal $cover$ value, select the one with the highest confidence for that state.
• For rules with equal $conf$ value, choose the one with higher $cosine$ value as the state’s association rule.

Figure 4 illustrates the process of determining current device status using the monitoring dataset.

After mining electrical equipment state evaluation data, a Naive Bayes classifier assesses observation data of unknown states. The Naive Bayes classifier determines device states as follows.

Let $T=\{x_1,x_2,\dots ,x_k\}$ be the training set of elements and related class labels, where each unit is an n-dimensional vector $x_1=[a_1,a_2,\dots ,a_{\mathrm{n}}]$.

Calculate the conditional probability of $x_{\mathrm{i}}$ for each given feature X in different categories n times based on the $a_{\mathrm{j}}$ attribute. By

$$P(x_{\mathrm{i}}|X)={\displaystyle \frac{P\left(X\right|x_{\mathrm{i}})·P(x_{\mathrm{i}})}{P\left(X\right)}}$$

(13)

The probability of the feature belonging to a specific state is calculated, then determines the probability of each state.

$$P\left(C_k\right|X)\propto P(C_k){\prod }_{i=1}^{n}P\left(x_{\mathrm{i}}\right|X)$$

(14)

The final prediction synthesizes these results [32,33].

Figure 5 shows the flowchart of this process.

2.5. Case Study

This paper aims to evaluate the quality of various electrical equipment in a substation. Data from a 110 kV substation, operated by a power supply company was used to analyze the effectiveness of data mining-based state evaluation for electrical equipment. The 110 kV substation is equipped with: (1) Two 110 kV incoming lines with GIS, including three sets of circuit breakers and isolation switches on both sides, three sets of current transformers, two capacitive line voltage transformers, one set of 110 kV bus voltage transformers and lightning arresters. (2) A 50 MVA main transformer (3) Seven 10 kV outgoing lines with supporting electrical equipment using armored movable indoor AC metal-enclosed switchgear. Each outgoing cable is equipped with a parallel lightning arrester at its front end. (4) A 10 kV bus is connected to station power transformers, bus voltage transformers, and two sets of capacitor banks.

(1)

Effectiveness analysis

The GIS was used to validate the proposed electrical equipment state evaluation methods. Data from various sources, including online monitoring, testing, operation, maintenance, and environmental factors, were used to assess its operational status. This approach assumes that all data accurately reflect the real state of the equipment. The dataset was split into a training set (70%) and a test set (30%). The training set was used to identify key factors influencing equipment quality and to uncover the influence mechanisms and strong association rules. The test set was used to evaluate the quality assessment methodology, thereby validating its accuracy.

The study dataset includes GIS data samples from three sources: routine tests, online monitoring, and inspections. The correct functioning of GIS depends on four main components: conductors, insulators, cooling medium and mobile contacts. In the data samples, beyond general environmental factors such as time, weather, temperature, and humidity, loop resistance and external contact temperature are used to represent conductive factors. The insulation resistance characteristics are used to account for the insulating factors. And the SF₆ moisture content and air pressure features accounts for cooling medium factors. The moving contact factor is reflected by operating time characteristics.

Table 3. Data sample characteristics.

Type	Label	Description	Number Range
Test	Operation time	Breaking time refers to the interval between the initiation of the breaking operation and the complete separation of all pole contacts. Closing time is defined as the interval from the energization of the closing circuit to the complete contact of all pole contacts. Synchronicity of operations encompasses the timing of opening and closing actions, three-phase breakage, and the instantaneous time differences between contacts.	Opening: [27.4, 104.7] Closing: [53.2, 126.8] Synchronism: [0.4%, 7.2%]
	Loop resistance	Contact resistance in a circuit breaker is measured between its movable and static contacts, representing the resistance of the conductive circuit.	[87.3, 245.8]
	SF6 moisture content	If SF6 moisture content meet the required standards.	[63, 160]
Online monitoring	SF6 gas pressure	SF6 gas pressure, indicator of arc extinguishing capability.	[0.58, 0.7]
	Ambient temperature	Testing device temperature sensor to measure ambient temperature.	[−3, 42]
	Ambient humidity	Testing device humidity sensor to measure ambient humidity.	[22, 93]
Inspection	SF6 gas pressure	Circuit breaker gas pressure, measured by the supplied gauge.	[0.58, 0.7]
	External contact temperature	Infrared thermometer measurements: quantifies temperature at contact surfaces, indicating potential oxidation or poor contact.	[12, 128]
	Ambient temperature	Thermometer measurements.	[−12, 40]
	Ambient temperature	Hygrometer measurements.	[26, 96]

summarizes the features included in each data sample.

To investigate the interrelationships among various GIS status data in the substation environment, raw data samples were preprocessed using Gaussian mixture models before applying the a priori algorithm.

Table 4. High voltage electrical equipment quantification items.

Label		Parameters	Classification
L1	Opening and closing time (Test)	Closing < 70, opening < 35, synchronism < 2%	Normal (1A)
		70 < closing < 90, 35 < opening < 45, synchronism < 4%	Attention (1B)
		Closing ≥ 70, opening ≥ 35, synchronism ≥ 4%	Abnormal (1C)
L2	Circuit resistance (Test)	<130	Normal (2A)
		[130, 160]	Attention (2B)
		>160	Abnormal (2C)
L3	SF6 moisture content (Test)	<90	Normal (3A)
		[90, 150]	Attention (3B)
		>150	Abnormal (3C)
L4	Gas pressure (Online monitoring)	>0.68	Normal (4A)
		[0.65, 0.68]	Attention (4B)
		<0.65	Abnormal (4C)
L5	Gas pressure (Inspection)	>0.68	Normal (5A)
		[0.65, 0.68]	Attention (5B)
		<0.65	Abnormal (5C)
L6	External contact temperature (Inspection)	<20	Normal (6A)
		[20, 50]	Attention (6B)
		>50	Abnormal (6C)
L7	Ambient temperature (Inspection)	[10, 30]	Moderate temperature (7A)
		>30	High temperature (7B)
		<10	Low temperature (7C)
L8	Ambient humidity (Inspection)	[30, 80]	Moderate (8A)
		>80	Moist (8B)
		<30	Dry (8C)

shows the distribution of data processed by the Gaussian mixture model. The internal structure and features of the data are described based on the center position and distribution shape of each cluster [34].

The primary finding was that specific combinations of conditions correlate with particular states of electrical equipment quality.

Table 5. Association rules extracted from Table 4 (excerpt).

Rule	$\mathit{C}\mathit{o}\mathit{n}\mathit{f}$ (%)	Reasons	Result
1	91.556	L1 = 1A and L7 = 7A and L8 = 8A	A
2	89.784	L1 = 1B and L7 = 7A and L8 = 8A	B
3	81.846	L1 = 1B and L7 = 7C and L8 = 8B	C
4	100	L1 = 1C	C
5	92.485	L2 = 2A and L7 = 7A and L8 = 8A	A
6	82.31	L2 = 2B and L7 = 7B and L8 = 8A	A
7	85.661	L2 = 2B and L8 = 8A	B
8	100	L2 = 2C	C
9	92.766	L3 = 3A and L7 = 7A and L8 = 8A	A
10	81.523	L3 = 3A and L8 = 8B	B
11	100	L3 = 3C	C
12	100	L4 = 4C and L5 = 5C	C
13	100	L4 = 4A and L5 = 5A	A
14	100	L4 = 4B and L5 = 5B	B
15	95.647	L6 = 6A and L7 = 7A	A
16	90.112	L6 = 6B and L7 = 7C and L8 = 8A	B

presents selected association rules extracted from the dataset using the a priori algorithm. The minimum support $Minsup$ and minimum confidence $minconf$ thresholds were set to 4% and 80%, respectively. The support, confidence, and lift metrics of the rules depend on data balancing and mixing processes. The prefix number for each variable indicates the attribute index, which is applicable to repeated transactions with distinct attributes. Rules extracted based on these thresholds are considered reliable and useful, as the statistical relationships between antecedents and consequents are validated in the main unbalanced dataset. However, the metrics of rule support, confidence, and lift are valid only within the respective sub-datasets created through record relabeling and balancing.

Table 5 provides evaluation criteria for the rules. For instance, the first four rules suggest that temperature and humidity significantly influence the on–off performance of switches. In humid summer conditions, slightly exceeding the on–off time may cause equipment failure, even without affecting usage. Severely exceeding the on–off time will inevitably lead to equipment issues. The pressure of SF₆ consistently aligns with both human observations and equipment testing results. These parameters can be quickly assessed through equipment testing in emergency situations, reducing decision-making time. The temperature of the equipment’s external contacts is influenced by ambient environment and equipment load, rather than solely the contact surface condition. In high-temperature conditions, the equipment’s temperature rises due to elevated ambient temperature, increased cooling load from air conditioning and other devices further contributes to additional heat generation in conductors.

Naive Bayes classification calculates the posterior probability of a sample belonging to a specific category based on available evidence. The sample is then assigned to the category with the highest posterior probability. This discussion focuses solely on probability parameters, as the Naive Bayes classifier does not require learning structural parameters. The trained Bayes classifier processes the test dataset by determining the posterior probability of states based on association rules between mined states and metrics (Equations (13) and (14)). Using the data mining model to determine the a priori probability. The model’s effectiveness is validated by comparing its detection criteria, based on the attributes of derived rules, with the state parameters of the test sample set. Figure 6 illustrates the prediction results of the test set.

Figure 6 compares the predictive evaluation model with the actual dataset. In this figure, horizontal axis represents the labeling of test samples, and vertical axis represents the quality of the electrical equipment. The symbol ‘-’ denotes equipment quality recorded in data samples, ‘|’ represents the results obtained by using the fusion proposed in this paper of the a priori algorithm with Naive Bayes classification. And ‘o’ represents the results obtained using a priori algorithm alone. Comparative analysis reveals that the proposed algorithm achieves an accuracy of 96.68%, surpassing the a priori algorithm’s accuracy of 89.21%. These results indicate strong consistency with the training dataset, improved electrical equipment status prediction. Furthermore, there is significantly enhanced accuracy of the proposed method compared to the a priori algorithm alone.

(2)

Comparison and analysis of effectiveness

To compare the effectiveness of the proposed electrical equipment condition assessment method with other classifier algorithms, we used data from various sources related to the main transformer, including online monitoring, testing, operation and maintenance, and environmental factors. Next followed the process described in (1), using 70% of the dataset as a training set and 30% as a test set for quality assessment of the electrical equipment. Then, we compared our method’s effectiveness with other classifier algorithms using various performance metrics to predict the main transformer results: accuracy, recall, precision, F1-score, receiver operating characteristic (ROC) curve, and area under the curve (AUC).

Table 6. Distribution of processed data.

Label		Description	Parameter	Classification
L1	Absorptance (Test)	Insulation resistance ratio: measured using a 2500 V megger, comparing winding resistance at 60 s and 15 s of pressurization.	>1.8	Normal (1A)
			[1.3, 1.8]	Attention (1B)
			<1.3	Abnormal (1C)
L2	DC resistance (Test)	Phase winding DC resistance: calculated as the deviation of each phase from the three-phase average value.	<1%	Normal (2A)
			[1%, 2%]	Attention (2B)
			>2%	Abnormal (2C)
L3	Ratio test (Test)	Tap changer voltage ratio: expressed as the deviation from the rated tapping voltage ratio for each tap position.	<0.5%	Normal (3A)
			[0.5%, 1%]	Attention (3B)
			>1%	Abnormal (3C)
L4	Gas content of oil (Online monitoring)	Volume fraction of gases in transformer oil, resulting from thermal and moisture effects.	<2%	Normal (4A)
			[2%, 5%]	Attention (4B)
			>5%	Abnormal (4C)
L5	Oil temperature (Inspection)	Measured at the upper oil level during transformer operation.	<85	Normal (5A)
			[85, 100]	Attention (5B)
			>100	Abnormal (5C)
L6	Ground current (Online monitoring)	Measured on the iron core lead wire at the single grounding point of the transformer core.	<55	Normal (6A)
			[55, 80]	Attention (6B)
			>80	Abnormal (6C)
L7	External contact temperature (Inspection)	Infrared thermometer measurements: quantifies temperature at contact surfaces, indicating potential oxidation or poor contact.	<20	Moderate temperature (7A)
			[20, 50]	High temperature (7B)
			>50	Low temperature (7C)
L8	Oil indicator (Inspection)	Readings from the transformer’s oil level gauge and oil thermometer.	Oil temperature < 85, oil level [35%, 75%]	Normal (8A)
			Oil temperature [85, 100], oil level < 35%, or >75%	Attention (8B)
			Oil temperature > 100, oil level < 25%, or >90%	Abnormal (8C)
L9	Ambient temperature (Inspection)	Thermometer measurements.	[10, 30]	Moderate temperature (9A)
			>30	High temperature (9B)
			<10	Low temperature (9C)
L10	Ambient humidity (Inspection)	Hygrometer measurements.	[30, 80]	Moderate (10A)
			>80	Moist (10B)
			<30	Dry (10C)

shows the distribution of data processed by the Gaussian mixture model.

Table 7. Association rules extracted from Table 6 (excerpt).

Rule	$\mathit{C}\mathit{o}\mathit{n}\mathit{f}$ (%)	Reasons	Result
1	95.442	L1 = 1A and L9 = 9A and L10 = 10A	A
2	80.124	L1 = 1B and L9 = 9B	C
3	100	L1 = 1C	C
4	100	L2 = 2C	C
5	94.358	L4 = 4A and L9 = 9A and L9 = 9A	A
6	89.951	L4 = 4B and L9 = 9B	A
7	82.022	L4 = 4C and L5 = 5C	C
8	93.573	L7 = 7A and L9 = 9A and L10 = 10A	A
9	86.559	L7 = 7C and L9 = 9B	A
10	82.537	L7 = 7C and L9 = 9C	A

presents association rules mined using the method described in Section 2.4.

The method used these association rules to form probability parameters, then inputs the test dataset into a trained Naive Bayes classifier. The predicted results were organized into a 3 × 3 confusion matrix in Figure 7a. To evaluate the classifier’s performance, the project adjusted the statistical form to compare predicted and actual states, as shown in Figure 7b–d.

The confusion matrix has four metrics:

• True positive (TP): Both actual and predicted states belong to this state.
• True negative (TN): Neither actual nor predicted states belong to this state.
• False positive (FP): The predicted state belongs to this state, but the actual state does not.
• False negative (FN): The actual state belongs to this state, but the predicted state does not.

The performance metrics are calculated as follows:

$${\displaystyle \genfrac{}{}{0pt}{}{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}=\frac{TP}{ TP+FP}}{\begin{array}{c}\mathrm{Recall}=\frac{TP}{TP+FN}\\ \mathrm{Accurary}=\frac{TN+TP}{TN+TP+FN+FP}\\ \mathrm{F1-score}=2\times \frac{Precison\times Recall}{Precison+Recall}\end{array}}}$$

(15)

In the ROC curve, horizontal axis represents the false positive rate (FPR), proportion of incorrect predictions among samples with negative actual state. And vertical axis represents the true positive rate (TPR), proportion of correct predictions among samples with positive actual state. Performance is quantified by AUC, with higher values indicating better performance. The multiclass problem was transformed into three binary classification problems. For each category, the other categories were grouped together and an AUC value was calculated for each binary problem. These individual AUC values were combined to evaluate overall performance [35].

To compare the classifier’s performance with other models (e.g., Support Vector Machine (SVM) and K-Nearest Neighbor (KNN)), all experiments were conducted using MATLAB 2023a.

Figure 8 and Figure 9 display the confusion matrices for KNN and SVM, respectively. Figure 10 presents the ROC curves and AUC values for each model.

Table 8. Performance metrics for each method.

Classifiers	State	Accuracy	Precision	Recall	F1-Score
This method	Normal	93.06%	89.04%	90.28%	89.66%
	Attention	91.20%	86.30%	87.50%	86.90%
	Abnormal	97.22%	97.14%	94.44%	95.77%
SVM	Normal	92.59%	86.84%	91.67%	89.19%
	Attention	90.74%	87.14%	84.72%	85.91%
	Abnormal	98.13%	97.14%	94.44%	95.77%
KNN	Normal	92.59%	91.18%	86.11%	88.57%
	Attention	90.74%	83.12%	88.89%	85.91%
	Abnormal	96.76%	95.77%	94.44%	95.10%

summarizes the performance metrics across three states (normal, attention, and abnormal) for each model, with Figure 11 illustrating these metrics as a bar chart.

The proposed method demonstrates superior classification performance in normal and attention states. While its performance in abnormal states is marginally lower than the SVM model, it still outperforms in terms of accuracy and recall for abnormal states. The method’s superior performance is evidenced by higher AUC values and improved ROC curves, showing reduced FPR and enhanced TPR. This performance provides a reliable foundation for assessing electrical equipment reliability and informing decisions on shutdown, inspection, or maintenance requirements.

3. Conclusions

This study presents a data mining-based algorithm for evaluating electrical equipment status in substations. The algorithm combines the a priori and Naive Bayes algorithms to assess the current state of electrical equipment. The implementation of GMM for unifying electrical equipment state feature data enables more comprehensive data utilization compared to alternative evaluation methods. The a priori algorithm efficiently processes large-scale data, while the Bayes classifier utilizes the derived association rules for classification. This approach enhances accuracy in conditional probability estimation and improves overall classification performance. The proposed method’s applicability and effectiveness were assessed using diverse status monitoring data from operational substations. Results indicate the scheme’s viability for practical implementation in substation environments.

The feasibility of the proposed method was evaluated using statistical data from electrical equipment in a 110 kV substation of a power supply company. The evaluation process involved three steps: applying a Gaussian mixture model to analyze and discretize the GIS data, employing the a priori algorithm to derive frequent itemsets and association rules between electrical equipment quality and measurement data, and utilizing these rules to predict GIS quality through a Naive Bayes classifier. The method achieved a state prediction accuracy exceeding 95% when compared to the original dataset. Further evaluation using 110 kV arrester equipment data and a validity evaluation index demonstrated the superiority of the proposed classification method over other algorithms. Results showed that the proposed scheme outperforms single-category algorithms, demonstrating high accuracy and strong discriminative ability.

The complexity of electrical equipment status monitoring data and multiple influencing factors present significant challenges. As datasets grow, the number of candidates itemset for deriving association rules increases exponentially, escalating computational complexity. Moreover, while numerous association rules may be generated, many could lack meaningful information, potentially complicating subsequent state classification. Future research will aim to optimize the model for applications in diverse and complex environments, focusing on addressing these identified challenges. In conclusion, this scheme exhibits considerable potential and practical value for evaluating the status of high-voltage electrical equipment in substations.